The hat shop in Santa Monica California where I got it claims that it's the hat that Jake and Elmo wear in the Blues Brothers (http://www.imdb.com/media/rm1724161536/tt0080455). It's manufactured by the Golden Gate Hat company. Apparently, the movie studios in Los Angeles frequently use their products.

For me it's a spiritual icon. It reminds me that, like Jake and Elmo, I'm on a (secret) mission from God :).